*Optimal Transport for the System of Isentropic Euler Equation*

**Michael Westdickenberg**

Georgia Institute of Technology

School of Mathematics

mwestatmath.gatech.edu

**Abstract**: The isentropic Euler equations form a system of
conservation laws modeling compressible fluid flows with constant
thermodynamical entropy. Due to the occurrence of shock
discontinuities, the total energy of the system is decreasing in time.
We review the second order calculus on the wasserstein space of
probability measures and show how the isentropic Euler equations can be
interpreted as a steepest descent equation in this framework. We
introduce a variational time discretization based on a sequence of
minimization problems, and show that this approximation converges to a
suitably defined measure-valued solution of the conservation law.
Finally, we present some preliminary results about the numerical
implementation of our time discretization.